Results 1 to 5 of 5

Math Help - Using area to evaluate the integral

  1. #1
    Junior Member
    Joined
    Dec 2008
    Posts
    31

    Using area to evaluate the integral

    Use an area to evaluate

    a^2
    ∫ 3x dx,
    a

    where a > 1

    Having some trouble with this, could someone explain to me how to do this?
    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by Murphie View Post
    Use an area to evaluate

    a^2
    ∫ 3x dx,
    a

    where a > 1

    Having some trouble with this, could someone explain to me how to do this?
    Thanks.
    Dear Murphie,

    First draw the graph of y=3x. Since \int_{a}^{a^2}3xdx represents the area of this graph from x=a to  x=a^2 you can get the area of the trapezium formed by the x-axis and the curve at the given region.

    Hope this will give you an idea to solve the problem.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2008
    Posts
    31
    is the area 1/2(a)a^2 = (a^3)/2?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,396
    Thanks
    1846
    No, it is not. Go back and do what Sudharaka said!

    What are the coordinates of the vertices of the trapezium (I would say "trapezoid")? What is the "height" of that trapezoid? What are the lengths of the two "bases" of the trapezoid? Do you know the formula for the area of a trapezoid?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Murphie View Post
    is the area 1/2(a)a^2 = (a^3)/2?
    Check this answer by doing the integration.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: January 1st 2012, 01:59 AM
  2. Replies: 2
    Last Post: August 31st 2010, 08:38 AM
  3. Replies: 1
    Last Post: June 2nd 2010, 03:25 AM
  4. evaluate the integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 13th 2010, 03:41 PM
  5. Replies: 1
    Last Post: November 28th 2009, 09:44 AM

Search Tags


/mathhelpforum @mathhelpforum